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arXiv · 2509.15119

The regularity of monomial ideals and their integral closures

Yijun Cui·Cheng Gong·Guangjun Zhu
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Abstract

Let $I$ be a monomial ideal in a polynomial ring $S=K[x_1,\ldots,x_n]$ over a field $K$ with $n=2$ or $3$, and let $\overline{I}$ be its integral closure. We will show that $\text{reg} (\overline{I}) \le \text{reg} (I)$. Furthermore, if $I$ is generated by elements of degree $d$, then $\text{reg} (I)=d$ if and only if $I$ has linear quotients.

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Yijun Cui, Cheng Gong, Guangjun Zhu. 2025-09-18. The regularity of monomial ideals and their integral closures. https://arxiv.org/abs/2509.15119

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